How do you simplify $12 a (a^{2} + b) - 5 b (b^{2} + a) + 9 b (b^{2} + a) - 3 a (a^{2} + b)$ $12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)$ ?

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How do you simplify $12 a (a^{2} + b) - 5 b (b^{2} + a) + 9 b (b^{2} + a) - 3 a (a^{2} + b)$ $12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)$ ?

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Answer 1 · 2017-09-20T21:00:02

$9 a^{3} + 13 a b + 4 b^{3}$ $9a^3 +13ab +4b^3$

Explanation:

Step one : Expand the brackets

$12 a (a^{2} + b) - 5 b (b^{2} + a) + 9 b (b^{2} + a) - 3 a (a^{2} + b) =$ $12a(a^2+ b) - 5b(b^2+a) + 9b(b^2 + a) - 3a(a^2 +b) =$

$(12 a) (a^{2}) + (12 a) (b) (- 5 b) (b^{2}) + (- 5 b) (a) + (9 b) (b^{2}) + (9 b) (a) (- 3 a) (a^{2}) + (- 3 a) (b) =$ $(12a)(a^2) + (12a)(b) (-5b)(b^2)+(-5b)(a)+(9b)(b^2)+(9b)(a)(-3a)(a^2)+(-3a)(b) =$
which gives us

$12 a^{3} + 12 a b - 5 b^{3} - 5 a b + 9 b^{3} + 9 a b - 3 a^{3} - 3 a b$ $12a^3+12ab-5b^3-5ab+9b^3+9ab-3a^3-3ab$

Step two : Collect like terms

$12 a^{3} - 5 b^{3} - 5 a b + 9 b^{3} + 9 a b - 3 a^{3} - 3 a b = 9 a^{3} - 5 b^{3} - 5 a b + 9 b^{3} + 9 a b - 3 a b$ $color(red)(12a^3)-5b^3-5ab+9b^3+9ab color(red)( -3a^3)-3ab= color(green)(9a^3)-5b^3-5ab+9b^3+9ab-3ab$
$9 a^{3} + 12 a b - 5 b^{3} - 5 a b + 9 b^{3} + 9 a b - 3 a b = 9 a^{3} + 13 a b - 5 b^{3} + 9 b^{3}$ $9a^3+color(red)(12ab)-5b^3color(red)(-5ab)+9b^3color(red)(+9ab) color(red)(-3ab) = 9a^3 + color(green)(13ab)-5b^3+9b^3$
$9 a^{3} + 13 a b - 5 b^{3} + 9 b^{3} = 9 a^{3} + 13 a b + 4 b^{3}$ $9a^3+13abcolor(red)(-5b^3)+color(red)(9b^3)= 9a^3 +13ab +color(green)(4b^3)$

Answer:
$9 a^{3} + 13 a b + 4 b^{3}$ $9a^3 +13ab +4b^3$

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How do you simplify $12 a (a^{2} + b) - 5 b (b^{2} + a) + 9 b (b^{2} + a) - 3 a (a^{2} + b)$ $12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)$ ?

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How do you simplify 12a(a2+b)−5b(b2+a)+9b(b2+a)−3a(a2+b)12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)?

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How do you simplify $12 a (a^{2} + b) - 5 b (b^{2} + a) + 9 b (b^{2} + a) - 3 a (a^{2} + b)$ $12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)$ ?